{
  "id": "1011.3454",
  "version": "v1",
  "published": "2010-11-15T17:12:03.000Z",
  "updated": "2010-11-15T17:12:03.000Z",
  "title": "Arithmetic properties of centralizers of diffeomorphisms of the half-line",
  "authors": [
    "Helene Eynard"
  ],
  "comment": "20 pages, 8 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r_f its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1_f is always a one-parameter group, naturally identified to \\R, (with f identified to 1). On the other hand, Z^r_f, for r greater or equal to 2, can be smaller: in [Se], Sergeraert constructed an f whose C^infty centralizer reduces to the infinite cyclic group generated by f (i.e Z^\\infty_f identifies to \\Z). In [Ey1], we adapted Sergeraert's construction to obtain an f whose C^r centralizer, for all r between 2 and \\infty, contains a Cantor set K but is still strictly smaller than Z^1_f (= \\R). Here, we improve [Ey1] to construct, for any Liouville number alpha, an f as above such that, in addition, alpha belongs to K.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-15T17:12:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "57R50"
    ],
    "keywords": [
      "arithmetic properties",
      "liouville number alpha",
      "smooth diffeomorphism",
      "well-known results",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.3454E"
    }
  }
}